My first Cycles to Eevee render looks wrong. Tried many things to improve.. failed!
Try baking a denser and smaller area for your light volume. This should resolve some of the shadows better. I'd also set up lights specifically for Eevee, since the lights from Eevee are not 1:1 with Cycles. If you're not already, turn on soft shadows as well in your shadows option. If you've got subsurface scattering in your scene, make sure it's properly set up within Eevee as well by turning it on.

Edit

Here are the settings for the Irradience Volume, note the XYZ resolution.